On ideal equal convergence
Rafał Filipów ; Marcin Staniszewski
Open Mathematics, Tome 12 (2014), p. 896-910 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:268976 
@article{bwmeta1.element.doi-10_2478_s11533-013-0388-4,
     author = {Rafa\l\ Filip\'ow and Marcin Staniszewski},
     title = {On ideal equal convergence},
     journal = {Open Mathematics},
     volume = {12},
     year = {2014},
     pages = {896-910},
     zbl = {1315.40004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0388-4}
}

Rafał Filipów; Marcin Staniszewski. On ideal equal convergence. Open Mathematics, Tome 12 (2014) pp. 896-910. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0388-4/

[1] Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472 | Zbl 0405.26006

[2] Császár Á., Laczkovich M., Some remarks on discrete Baire classes, Acta Math. Acad. Sci. Hungar., 1979, 33(1–2), 51–70 http://dx.doi.org/10.1007/BF01903381 | Zbl 0401.54010

[3] Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177

[4] Filipów R., Szuca P., Three kinds of convergence and the associated -Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9 http://dx.doi.org/10.1016/j.jmaa.2012.02.041 | Zbl 1247.26007

[5] Hernández-Hernández F., Hrušák M., Cardinal invariants of analytic P-ideals, Canad. J. Math., 2007, 59(3), 575–595 http://dx.doi.org/10.4153/CJM-2007-024-8 | Zbl 1119.03046

[6] Kostyrko P., Šalát T., Wilczyński W., -convergence, Real Anal. Exchange, 2000/01, 26(2), 669–685

[7] Mačaj M., Sleziak M., -convergence, Real Anal. Exchange, 2010/11, 36(1), 177–193

[8] Todorčevic S., Analytic gaps, Fund. Math., 1996, 150(1), 55–66 | Zbl 0851.04002